## Skyhooks

### Skyhooks

i have tried but i don't understand why space elevators would have to be *over* the equator. Isn't it just as easy to 'hang' the top anywhere else? Could someone explain please?

They are such a good idea, i really don't see why we don't put a lot more money into devloping the technology needed. The cost of getting small amounts of stuff into orbit is ridiculously high, especially with the end of the shutttle.

Patchwork cat
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The top is a small mass that rotates around a big mass, the earth. The earth is rotating itself around its axis, which is perpendicular to the equator.

The top has to move to the same direction as the rotation of the earth, otherwise it wouldn't be fixed relative to the station at the bottom (and I can imagine the cable can be stretched only so much). The only orbit where this is possible is above the equator, because the top rotates around the center of mass of the earth.

The top isn't fixed anywhere, so due to gravitation it will fall towards the earth. To offset this free fall, it has to move at a certain fixed speed to remain in its orbit. This speed depends on the height of the orbit. In order for the top to be geostationary, the speed must also be the same as the speed of the rotation of the earth. This is only the case at a certain height, at 35,786 km. So the orbit where you can put an elevator top is pretty much fixed.

http://en.wikipedia.org/wiki/Geostationary
Buck
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What I wonder is, what keeps the generators in place? A lot of the energy probably goes into keeping them where they are, relative to the surface.
Buck
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Christ, that must take a lot of power.

Kesh
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Trying a different tack, at the equator, the circle (or ellipse) of the orbit stays directly over the equator. If you start north or south of the equator, the orbit still has to be centered over the center (of mass) of the earth, so it would be tilted.

If at the right distance from the centre of the earth, the elevator would stay (mostly) at the right longitude, but would want to move north and south of the equator like a pendulum, its position forming that slightly out-of-kilter figure-eight shape called an analemma.

An equatorial orbit shrinks that analemma to (almost) a single point.
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DetailBear
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Since this is one of the few forums where I doubt I'll get ambushed for grammatical nitpicking... The satellite revolves around the Earth. (I'm sure it rotates, too, so that the bottom is always facing the Earth, but my guess is that its revolution was the important part of the discussion here.)
GreatLimmick
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Another thing thats limiting the development of space elevators would be the strength of the cable needed, theres a trade off between strength and weight.

Currently for our world, materials are not strong enough to take such forces, but research is being done on carbon nanotubes and other composite materials, another problem is how to assemble such a structure, it might have to be from space, placing the station in geostationary orbit and 'hanging' the cable down from space...(with the cost of conventional rocketry needed to produce the first one), or an approach where the top section is hung down from space and the bottom floated up on balloons meeting somewhere in the middle.

Other problems would be how the elevator car would ascend the cable, what to do if the cable snapped (and what to do if there were people on it) and other small things that currently make space elevators unfeasible currently in our world.
KC

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It also would be a good idea to look at the Wikipedia article on this subject, which I used mostly to get the term "geostationary", which distinguishes an equitorial, earth-stationary orbit from a non-equatorial geosynchronous orbit.

Of course once I got to the article I started using it as source material for the LongShot story...
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Allan_ecker
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GreatLimmick wrote:Since this is one of the few forums where I doubt I'll get ambushed for grammatical nitpicking... The satellite revolves around the Earth. (I'm sure it rotates, too, so that the bottom is always facing the Earth, but my guess is that its revolution was the important part of the discussion here.)

Actually, since I'm not a native speaker, I'm grateful for grammatical nitpicking. Although in this case I should have noticed, because "rotate" is pretty much the same word in German.
Buck
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KaiAdin wrote:Another thing thats limiting the development of space elevators would be the strength of the cable needed, theres a trade off between strength and weight.

Currently for our world, materials are not strong enough to take such forces, but research is being done on carbon nanotubes and other composite materials, another problem is how to assemble such a structure, it might have to be from space, placing the station in geostationary orbit and 'hanging' the cable down from space...(with the cost of conventional rocketry needed to produce the first one), or an approach where the top section is hung down from space and the bottom floated up on balloons meeting somewhere in the middle.

Which is why i bemoan the lack of money being invested. I love Carbon molecules, anything called a Buckyball has to be good! Arthur Clarke invented the idea ages ago and we have since piled money into rockets and space shuttles. Considering ACC's other ideas that have come to fruition, you'd think someone in power would have seen the advantages before now. :(
i looked at Wiki first btw, i always do. This thread looks better than that page and thanks for that. i still don't quite understand though, i expect i will, but then i still don't quite get relativity. M theory yes, relativity no. Strange...

Patchwork cat
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### Great time waster

Gravity Chaos

"Drag or gently toss the spheres below and see what happens."

Large file. Flash required.
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DetailBear
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Tut tut, DB, that's Newtonian gravity simulation!

Now it takes some doing even to figure out why time slows down as one approaches the speed of light, let alone figure out how the twins paradox can work if all references are equally valid.

Actually I still can't figure that one out... I mean... if all frames are equally valid then how does the universe know which twin actually did the accelerating?
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Allan_ecker
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Determining which twin experienced acceleration seems rather straightforward to me. If they started on a planet, one of them had to be accelerated into orbit. If they started in free fall, only one of them experienced an accelerating force. Either way, the one who actually moved had to be moved in one direction for a while, then brake, then move in the other direction for a while, then brake again. Maybe it could be expressed as a change in inertial frame of reference?
GreatLimmick
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It's an Occam's Razor sort of thing. Either one twin and his vehicle was accelerated out and back, or the other twin, the planet and the entire universe was accelerated the other way and back. Both are equally valid theoretically, until you calculate the energy to move all that mass.

Empirically, the younger one moved.

And my link was about orbits, not relativity, but you knew that.
HUGS = Huge, Unrestrained, Genial Squeezings.

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DetailBear
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Hm. It's probably a kinetic energy thing as you say. Since I don't have the actual equations but only an "intuitive" description of what happens when light zips by someone (it always has to appear to move at the same rate) I can't be sure. However I'd be willing to bet that if you took the equations and re-organized it so that the universe moved instead, the differing masses and energies would end up flipping everything around so that the minus signs landed where they needed to for the fast-flying twin to stay young.

Which is good to know since that's how time travel works...
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Allan_ecker
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allan_ecker wrote:Actually I still can't figure that one out... I mean... if all frames are equally valid then how does the universe know which twin actually did the accelerating?

Well, the acceleration can be measured. As long as the twins move away from each other at constant speed, all frames are equally valid. At one point, however, one of the twins changes direction to "return", which involves acceleration.

Quantum mechanics is much weirder.
Buck
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DetailBear wrote:It's an Occam's Razor sort of thing. Either one twin and his vehicle was accelerated out and back, or the other twin, the planet and the entire universe was accelerated the other way and back. Both are equally valid theoretically, until you calculate the energy to move all that mass.

Empirically, the younger one moved.

And my link was about orbits, not relativity, but you knew that.

allan_ecker wrote:Hm. It's probably a kinetic energy thing as you say. Since I don't have the actual equations but only an "intuitive" description of what happens when light zips by someone (it always has to appear to move at the same rate) I can't be sure. However I'd be willing to bet that if you took the equations and re-organized it so that the universe moved instead, the differing masses and energies would end up flipping everything around so that the minus signs landed where they needed to for the fast-flying twin to stay young.

Which is good to know since that's how time travel works...

I'm not so sure about all that. Let's take the simplest case, where the twins start in free-fall, one of them is stationary, and one of them is accelerated. Only one twin experiences an accelerating force. This force is a measurable physical quantity. No matter how much mathematical legerdemain you attempt, that force will still be applied to the same twin. So, he's the one whose inertial frame of reference is changing.

Let's look at another case. You take the same twins. One of them is accelerated nearly to the speed of light, and then stops. Then the other one experiences the exact same acceleration-- he's brought to the same velocity at the same rate, maintains it for the same amount of subjective time, and then brakes at the same rate. The two of them have experienced the exact same change in inertial frame of reference and, although I don't have the equations to do the calculations, I'd be willing to bet that they will be the same age when they meet up. In a slightly more complicated case, if you send them in opposite directions at the same speed (and same magnitude of acceleration), I'd be willing to bet they'll be the same age when they meet up again because they've experienced the same magnitude of change in inertial frame of reference.
GreatLimmick
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Bah, frames of reference are intrinsically confusing. What if one twin is standing on the Earth, and one is accelerating in a rocket at one gee?

Aren't they both in the same reference?

And Quantum Mechanics are easier for me because I'm more familiar.

So electrons get caught in delecate little three-dimensional potential wells, oscillating off of their "walls" to create the characteristic "orbitals" we all know and love, so what? Band theory of solids? Cake. Diode junctions and built-in electric fields? Phonons? The Photoelectric effect? All easy.

But a guy in a rocket? That stuff just messes me up, man.
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"Death and taxes are unsolved engineering problems."
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Allan_ecker
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I did some thinking at work tonight, and it occurred to me that an inertial frame of reference is nothing more than a vector of force, whether it's due to gravity, a combustion engine, or a rocket. So, the twin who can be considered to have moved is simply the one who experienced the greatest change in the force acting on him. It makes sense, once you think about the fact that a clock at a higher altitude (experiencing less gravitational force) keeps different time than an identical clock at a lower altitude (experiencing more gravitational force). I forget which one runs faster, and I'm kind of tired, so I'm not sure I could puzzle it out exactly, but I wish I had a way to gracefully end this post without it looking like I completely forgot what I was talking about.
GreatLimmick
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AH. DELTA f.

Much better.

AutoGenesis still sucking balls however. *rattles fist at un-updated page*
<A HREF="http://umlauthouse.comicgenesis.com" TARGET=_blank>UH2: The Mayhem of a New Generation</A>

"Death and taxes are unsolved engineering problems."
--Romano Machado

Allan_ecker
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